EXTENDED KALMAN FILTERING FOR VORTEX SYSTEMS - PART-II - RANKINE VORTICES AND OBSERVING-SYSTEM DESIGN

Point-vortex systems with both regular and chaotic motion can be track ed by a combination of Lagrangian observations of vortex position and of Eulerian observations of fluid velocity at a few fixed points. If o nly Eulerian observations are available, singularities in the tracking can develop due to nonlinearity in the observing functions on two occ asions: when point vortices pass very close to an observing station, a nd when the observed speed is small. In Part II of this two-part paper , the vorticity concentrations are approximated by Rankine vortices wi th finite core in solid-body rotation, while a cut-off criterion is im posed on the Eulerian observations; this removes the singularities and hence results in satisfactory tracking when the observations are judi ciously chosen. The main result is that a number of observations compa rable to that of the distinct vorticity concentrations suffices for ve ry accurate tracking. The key elements for successful tracking of Rank ine-vortex systems using nonlinear, Eulerian observations are: distrib ution of available stations, threshold criteria for the selection of s tations used in each update, and the observing frequency. Simple analy sis provides the optimal estimate for these key elements, together wit h the optimal size of the estimated Rankine vortices. (C) 1997 Elsevie r Science B.V.